论文标题
映射班级的歧管组，看起来像$ 3 $维
Mapping class group of manifolds which look like $3$-dimensional complete intersections
论文作者
论文摘要
在本文中，我们计算了一个封闭的简单连接的6个manifolds $ m $的映射类小组，看起来像完整的交叉点，即〜e。我们确定映射类组的一些代数属性；例如，我们计算其Abelianization及其中心。我们证明了中心映射类组的Modulo是残留有限的，几乎不含扭转。我们还研究低维同源组。结果与Riemann表面的映射类组的计算非常相似。我们给出了映射类组的生成器，以及在$π_{3}（m）$上琐碎作用的子组的生成器和关系。
In this paper we compute the mapping class group of closed simply-connected 6-manifolds $M$ which look like complete intersections, i.~e.~ $H_2(M;\mathbb Z) \cong \mathbb Z $ and $x^3 \ne 0$ where $x \in H^2(M; \mathbb Z)$ is a generator. We determine some algebraic properties of the mapping class group; for example we compute its abelianization and its center. We show that modulo the center the mapping class group is residually finite and virtually torsion-free. We also study low dimensional homology groups. The results are very similar to the computation of the mapping class group of Riemann surfaces. We give generators of the mapping class group, and generators and relations for the subgroup acting trivially on $π_{3}(M)$.
